1. Class 12 Financial Management, 15.414 Discount rates

2. MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Today Discount rates Using the CAPM Estimating beta and the cost of capital Reading Brealey and Myers, Chapter 9 Graham and Harvey (2000, p. 1 – 10)

3. Review MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 The CAPM Measuring risk A stock’s systematic risk is measured by beta, the slope when the stock return is regressed on the market: Required returns Investors should be compensated for bearing non-diversifiable, beta risk. The required return on a stock is: Market risk premium

4. The risk-return trade-off MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Slope = E[R M ] – r f Market portfolio (β = 1) Stock's beta Stock's expected return

5. Using the CAPM MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Valuation Discount rate The rate of return that investors demand on investments with the same level of risk. CAPM Risk = the project’s beta Discount rate = r f + β project E[R M – r f ]

6. Practical issues Using the CAPM MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 1: How can we estimate the project’s beta? 2: What is the riskfree rate and the market risk premium? 3: How does debt affect risk and the cost of capital? 4: Additional risk factors?

7. Example MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 It’s 1979. Southwest Airlines, a growing start-up, has been profitable as the low-cost airline in the Texas market. Southwest is thinking about expanding to other U.S. cities. Management forecasts that the expansion will cost $100 million over the next few years but will lead to strong future growth ($ millions): Year Sales Growth is expected to slow to 10% annually after 1982. What cost of capital should Southwest use to evaluate the proposed expansion?

8. Southwest stock price, 1970 – 1979 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12

9. Issue 1 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 How can we estimate the project’s beta? What factors are important? Two approaches Estimate the firm’s beta Estimate the industry’s beta (comparables) How much data? 5 – 10 years of monthly data

10. Estimating beta MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 1: Estimate the firm’s beta Advantage If the project has the same risks as the firm (an expansion), this approach measures exactly what we want Disadvantages Generally not very precise (high standard error) Firm’s beta might change over time Can’t be used for projects in a new line of business or for diversified firms

11. Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Is this approach useful for SW? Is the risk (beta) of the expansion likely to be the same as the beta of the firm? Is Southwest’s past beta likely to be a useful guide for the future beta of the project? Southwest, 1973 – 1979 (84 months) Estimate: β SW = 1.25 (std error = 0.31); R 2 = 0.16 [R M = return on a market index, like S&P 500]

12. Southwest vs. Total U.S. market return MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 SW return Slope = 1.25 Mkt return

13. Southwest’s beta over time MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 SW return Mkt return

14. Estimating beta MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 2: Estimate the industry’s beta* Advantages Beta estimated more precisely. Appropriate if the project is in a new line of business. Disadvantages Do the firm’s really have the same risk as the project? Do they serve different markets? Do they have more debt? Do they have the same cost stucture? * Estimate the betas of individual firms and then average, or estimate the beta of an industry portfolio.

15. Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Is this approach useful for SW? Is the risk (beta) of the expansion likely to be the same as the beta of other airlines? Airline betas, 1973 – 1979 Airline American Continental Delta Northwest United USAir Average = 1.36, standard error of 0.13

16. Airline industry vs. Total U.S. market return MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Airline Industry return Slope = 1.36 Mkt return

17. Issue 2 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Riskfree rate? Should the riskfree rate be the short-term Tbill rate or the long-term Tbond rate? Match horizons If short-lived project, use Tbill rate If long-lived project, use Tbond rate (say, 10-year) Riskfree rate changes a lot over time 1979: Tbill rate = 9.65%, Tbond rate = 10.39% 2003: Tbill rate = 0.93%, Tbond rate = 4.31%

18. Interest rates, 1953 – 2001 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12

19. Issue 2 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Market risk premium? Historical estimates 1872 – 1999: 5.73% (std error = 1.63%) 1926 – 1999: 8.26% (std error = 2.24%) 1963 – 1999: 6.44% (std error = 2.51%) r = DY + g 1872 – 1999: 3.64% (std error = 1.15%) 1872 – 1949: 3.79% (std error = 1.78%) 1950 – 1999: 3.40% (std error = 0.99%) Going forward? My guess, 4 – 6% Constant growth model

20. Market risk premium MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Survey of CFOs Source: Graham and Harvey, 2002

21. Cost of capital Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Firm’s beta: β SW = 1.25 Industry’s beta: β Airlines = 1.36 Riskfree rate = Tbond rate = 10.39% Market risk premium = 5.0% Discount rate* * If no debt

22. Issue 3 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Debt financing, part 1 If the firm has debt, the cost of capital (discount rate) is a weighted average of the costs of debt and equity financing. Cost of equity: Cost of debt: (2) r D = yield on the firm’s bon After-tax weighted average cost of capital

23. Balance sheet MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Current Assets Fixed Assets 1.Tangible fixed assets 2. Intangible fixed assets Current Liabilities Long-Term Debt Shareholders’ Equity

24. In 1979, Southwest was financed with 20% debt (debt / firm value). The borrowing rate was 11.4% and the tax rate was 35%. What is Southwest’s WACC? Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Cost of equity Weighted-average cost of capital Discount rate = 14.99%

25. Issue 3 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Debt financing, part 2 If firms have different debt ratios, we cannot directly compare the stock betas of firms in the same industry. Firms with higher leverage should have riskier equity Higher D/V → higher β E Complicates the use of industry betas. (1)Estimate equity betas for each firm (2) Calculate r E and WACC for each firm (3) Use the industry’s WACC to estimate the cost of capital for the project

26. Airline industry Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Airline American Continental Delta Northwest United USAir Equity betas Leverage ratios Airline American Continental Delta Northwest United USAir

27. The tax rate is 35%, r D = 11.4%, r f = 10.39%, and E[RM – r f ] = 5.0%. Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Airline American Continental Delta Northwest United USAir Average

28. Issue 4 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Multifactor models Beta might not fully summarize all relevant risks. Additional risk factors could be important. Measuring risk Regress R i on macroeconomic risk factors, F 1 … F K is firm i’s sensitivity to the factor. Expected returns Expected returns are linearly related to risk is the risk premium for factor k.

29. Fama-French 3-factor model* Multifactor models MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 CAPM misses risk factors associated with size and B/M What are the risks? R M = Market portfolio return SMB = Small stock return – Big stock return HML = High-B/M stock return – Low-B/M stock return *http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/

30. Betas, 1960 – 2001 MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 B/M portfolios Size portfolios Decile Low B/MSmallest High B/MLargest

31. Cost of capital Southwest MIT SLOAN SCHOOL OF MANAGEMENT 15.414Class 12 Cost of equity